I'm trying to figure out if I am doing this correctly.

Given the matrix A:

[1 -.5]

[.5 2]

write down e^(tA) and calculate e^(tA)X, X = (1,1)

So far what I did was, I found the eigenvalues (1.5 repeated) and the eigenvectors ( [-1 1], [1 1]). (The eigenvectors are transposed)

Then I set e^(tA) = T^(-1)AT, where T = [eigenvector1, eigenvector 2]

Which leads to e^(tA):

[1.75 .75]

[0 1.5]

I Feel that I do not have the correct equation for e^(tA), can anyone help me?